Abstract

We propose the use of binary slanted surface-relief gratings with parallel-groove walls as input and output couplers in a planar optical interconnect. Parametric optimization of cascaded output couplers is employed to design an interconnect consisting of N output couplers producing a uniform intensity distribution with a high efficiency that may be realized in one lithographic etching step. The sensitivity of a N = 4 interconnect to various fabrication errors is analyzed. We demonstrate the operation of a slanted surface-relief grating manufactured with electron-beam lithography and reactive-ion etching for an operating wavelength of λ = 0.633 μm.

© 1997 Optical Society of America

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  1. J. Jahns, A. Huang, “Planar integration of free-space optical components, ” Appl. Opt. 28, 1602–1605 (1989).
    [CrossRef] [PubMed]
  2. S. J. Walker, J. Jahns, “Optical clock distribution using integrated free-space optics, ” Opt. Commun. 90, 359–371(1992).
    [CrossRef]
  3. R. Petit, ed., Electromagnetic Theory of Gratings, Vol. 22 of Topics in Current Physics (Springer-Verlag, Berlin, 1980).
    [CrossRef]
  4. E. Noponen, A. Vasara, J. Turunen, J. M. Miller, M. R. Taghizadeh, “Synthetic diffractive optics in the resonance domain, ” J. Opt. Soc. Am. A 9, 1206–1213 (1992).
    [CrossRef]
  5. A. A. Friesem, Y. Amitai, “Planar diffractive elements for compact optics,” in Trends in Optics: Research, Developments and Applications, A. Consortini, ed. (Academic, San Diego, Calif., 1996), pp. 125–144.
  6. J. Turunen, F. Wyrowski, “Diffractive optics: from promise to fruition,” in Trends in Optics: Research, Developments and Applications, A. Consortini, ed. (Academic, San Diego, Calif., 1996), pp. 111–123.
  7. J. M. Miller, J. Turunen, E. Noponen, A. Vasara, M. R. Taghizadeh, “Rigorous modal theory for multiply grooved lamellar gratings, ” Opt. Commun. 111, 526–535(1994).
    [CrossRef]
  8. J. Saarinen, E. Noponen, J. Turunen, T. Suhara, H. Nishihara, “Asymmetric beam deflection by doubly grooved binary gratings, ” Appl. Opt. 33, 2401–2405 (1995).
    [CrossRef]
  9. E. Noponen, J. Turunen, A. Vasara, “Parametric optimization of multilevel diffractive optical elements by electromagnetic theory, ” Appl. Opt. 31, 5910–5912 (1992).
    [CrossRef] [PubMed]
  10. R. K. Kostuk, Y.-T. Huang, D. Hetherington, M. Kato, “Reducing alignment and chromatic sensitivity of holographic interconnects with substrate-mode holograms, ” Appl. Opt. 28, 4939–4944 (1989).
    [CrossRef] [PubMed]
  11. J. H. Yeh, R. K. Kostuk, “Free-space holographic optical interconnects for board-to-board and chip-to-chip interconnections, ” Opt. Lett. 21, 1274–1276 (1996).
    [CrossRef] [PubMed]
  12. S. Natarajan, C. Zhao, R. T. Chen, “Bi-directional optical backplane bus for general purpose multi-processor board-to-board optoelectronic interconnects, ” J. Lightwave Technol. 13, 1031–1040 (1995).
    [CrossRef]
  13. T. Nakaya, Y. Katoh, T. Kubota, M. Takeda, “Diffraction efficiency of a grating coupler for an array illuminator, ” Appl. Opt. 35, 3891–3898 (1996).
    [CrossRef] [PubMed]
  14. J. W. Parker, “Optical interconnection for advanced processor systems: a review of the esprit ii olives program, ” J. Lightwave Technol. 9, 1764–1773 (1991).
    [CrossRef]
  15. S. Paineau, J.-P. Ghesquiers, M. Charrier, T. Lemoine, “Clock distribution by holographic optical backplane in massively parallel processor architecture,” in Free Space Micro-Optical Systems (European Optical Society, Engelberg, Switzerland, 1996), pp. 52–53.
  16. J. M. Miller, N. de Beaucoudrey, P. Chavel, M. François, J. Turunen, “Inclined binary high-frequency gratings for an optical backplane interconnect,” in Proceedings of a Workshop on Diffractive Optics, Prague, Czech Republic, August 1995, pp. 33–34.
  17. N. de Beaucoudrey, J. M. Miller, P. Chavel, J. Turunen, “On the design and fabrication of high efficiency inclined binary high frequency gratings,” in Specification, Production, and Testing of Optical Components and Systems, A. E. Gee, J. Houee, eds., Proc. SPIE2775, 533–536 (1996).
  18. M. Takeda, T. Kubota, “Integrated optic array illuminator: a design for efficient and uniform power distribution, ” Appl. Opt. 30, 1090–1095 (1991).
    [CrossRef] [PubMed]
  19. D. Maystre, ed., Selected Papers on Diffraction Gratings, Vol. M583 of SPIE Milestone Series (SPIE Press, Bellingham, Wash., 1993), pp. xvii–xxx.
  20. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, London, 1989), pp. 705–708.
  21. N. Chateau, J.-P. Hugonin, “Algorithm for the rigorous coupled-wave analysis of grating diffraction, ” J. Opt. Soc. Am. A 11, 1321–1331 (1994).
    [CrossRef]
  22. A. Vasara, M. R. Taghizadeh, J. Turunen, J. Westerholm, E. Noponen, H. Ichikawa, J. M. Miller, T. Jaakkola, S. Kuisma, “Binary surface-relief gratings for array illumination in digital optics,” Appl. Opt. 31, 3320–3336 (1992).
    [CrossRef] [PubMed]
  23. L. A. Coldren, J. A. Rentschler, “Directional reactive-ion etching of InP with Cl2 containing gases, ” J. Vac. Sci. Technol. 19, 225–230 (1981).
    [CrossRef]
  24. T. Takamori, L. A. Coldren, J. L. Merz, “Angled etching of GaAs/AlGaAs by conventional Cl2 reactive ion etching,” Appl. Phys. Lett. 53, 2549–2551 (1988).
    [CrossRef]
  25. B. Jacobs, R. Zengerle, “Reactive ion etching of sloped sidewalls for surface emitting structures using a shadow mask technique,” J. Vac. Sci. Technol. B 14, 2537–2542 (1996).
    [CrossRef]
  26. J. M. Miller, N. de Beaucoudrey, P. Chavel, E. Cambril, H. Launois, “Synthesis of a subwavelength-pulse-width spatially modulated array illuminator for 0.633 μm,” Opt. Lett. 21, 1399–1401 (1996).
    [CrossRef] [PubMed]
  27. J. Bell, “Market misses message about diffractive optics,” Opto Laser Europe21–28 (March1997).
  28. E. Tervonen, J. Turunen, J. Pekola, “Pulse-frequency-modulated high-frequency-carrier diffractive elements for pattern projection,” Opt. Eng. 33, 2579–2587 (1994).
    [CrossRef]
  29. M. Li, A. Larsson, N. Eriksson, M. Hagberg, “Continuous-level phase-only computer-generated hologram realized by dislocated binary gratings,” Opt. Lett. 21, 1516–1518 (1996).
    [CrossRef] [PubMed]

1997 (1)

J. Bell, “Market misses message about diffractive optics,” Opto Laser Europe21–28 (March1997).

1996 (5)

1995 (2)

J. Saarinen, E. Noponen, J. Turunen, T. Suhara, H. Nishihara, “Asymmetric beam deflection by doubly grooved binary gratings, ” Appl. Opt. 33, 2401–2405 (1995).
[CrossRef]

S. Natarajan, C. Zhao, R. T. Chen, “Bi-directional optical backplane bus for general purpose multi-processor board-to-board optoelectronic interconnects, ” J. Lightwave Technol. 13, 1031–1040 (1995).
[CrossRef]

1994 (3)

J. M. Miller, J. Turunen, E. Noponen, A. Vasara, M. R. Taghizadeh, “Rigorous modal theory for multiply grooved lamellar gratings, ” Opt. Commun. 111, 526–535(1994).
[CrossRef]

E. Tervonen, J. Turunen, J. Pekola, “Pulse-frequency-modulated high-frequency-carrier diffractive elements for pattern projection,” Opt. Eng. 33, 2579–2587 (1994).
[CrossRef]

N. Chateau, J.-P. Hugonin, “Algorithm for the rigorous coupled-wave analysis of grating diffraction, ” J. Opt. Soc. Am. A 11, 1321–1331 (1994).
[CrossRef]

1992 (4)

1991 (2)

M. Takeda, T. Kubota, “Integrated optic array illuminator: a design for efficient and uniform power distribution, ” Appl. Opt. 30, 1090–1095 (1991).
[CrossRef] [PubMed]

J. W. Parker, “Optical interconnection for advanced processor systems: a review of the esprit ii olives program, ” J. Lightwave Technol. 9, 1764–1773 (1991).
[CrossRef]

1989 (2)

1988 (1)

T. Takamori, L. A. Coldren, J. L. Merz, “Angled etching of GaAs/AlGaAs by conventional Cl2 reactive ion etching,” Appl. Phys. Lett. 53, 2549–2551 (1988).
[CrossRef]

1981 (1)

L. A. Coldren, J. A. Rentschler, “Directional reactive-ion etching of InP with Cl2 containing gases, ” J. Vac. Sci. Technol. 19, 225–230 (1981).
[CrossRef]

Amitai, Y.

A. A. Friesem, Y. Amitai, “Planar diffractive elements for compact optics,” in Trends in Optics: Research, Developments and Applications, A. Consortini, ed. (Academic, San Diego, Calif., 1996), pp. 125–144.

Bell, J.

J. Bell, “Market misses message about diffractive optics,” Opto Laser Europe21–28 (March1997).

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, London, 1989), pp. 705–708.

Cambril, E.

Charrier, M.

S. Paineau, J.-P. Ghesquiers, M. Charrier, T. Lemoine, “Clock distribution by holographic optical backplane in massively parallel processor architecture,” in Free Space Micro-Optical Systems (European Optical Society, Engelberg, Switzerland, 1996), pp. 52–53.

Chateau, N.

Chavel, P.

J. M. Miller, N. de Beaucoudrey, P. Chavel, E. Cambril, H. Launois, “Synthesis of a subwavelength-pulse-width spatially modulated array illuminator for 0.633 μm,” Opt. Lett. 21, 1399–1401 (1996).
[CrossRef] [PubMed]

J. M. Miller, N. de Beaucoudrey, P. Chavel, M. François, J. Turunen, “Inclined binary high-frequency gratings for an optical backplane interconnect,” in Proceedings of a Workshop on Diffractive Optics, Prague, Czech Republic, August 1995, pp. 33–34.

N. de Beaucoudrey, J. M. Miller, P. Chavel, J. Turunen, “On the design and fabrication of high efficiency inclined binary high frequency gratings,” in Specification, Production, and Testing of Optical Components and Systems, A. E. Gee, J. Houee, eds., Proc. SPIE2775, 533–536 (1996).

Chen, R. T.

S. Natarajan, C. Zhao, R. T. Chen, “Bi-directional optical backplane bus for general purpose multi-processor board-to-board optoelectronic interconnects, ” J. Lightwave Technol. 13, 1031–1040 (1995).
[CrossRef]

Coldren, L. A.

T. Takamori, L. A. Coldren, J. L. Merz, “Angled etching of GaAs/AlGaAs by conventional Cl2 reactive ion etching,” Appl. Phys. Lett. 53, 2549–2551 (1988).
[CrossRef]

L. A. Coldren, J. A. Rentschler, “Directional reactive-ion etching of InP with Cl2 containing gases, ” J. Vac. Sci. Technol. 19, 225–230 (1981).
[CrossRef]

de Beaucoudrey, N.

J. M. Miller, N. de Beaucoudrey, P. Chavel, E. Cambril, H. Launois, “Synthesis of a subwavelength-pulse-width spatially modulated array illuminator for 0.633 μm,” Opt. Lett. 21, 1399–1401 (1996).
[CrossRef] [PubMed]

J. M. Miller, N. de Beaucoudrey, P. Chavel, M. François, J. Turunen, “Inclined binary high-frequency gratings for an optical backplane interconnect,” in Proceedings of a Workshop on Diffractive Optics, Prague, Czech Republic, August 1995, pp. 33–34.

N. de Beaucoudrey, J. M. Miller, P. Chavel, J. Turunen, “On the design and fabrication of high efficiency inclined binary high frequency gratings,” in Specification, Production, and Testing of Optical Components and Systems, A. E. Gee, J. Houee, eds., Proc. SPIE2775, 533–536 (1996).

Eriksson, N.

François, M.

J. M. Miller, N. de Beaucoudrey, P. Chavel, M. François, J. Turunen, “Inclined binary high-frequency gratings for an optical backplane interconnect,” in Proceedings of a Workshop on Diffractive Optics, Prague, Czech Republic, August 1995, pp. 33–34.

Friesem, A. A.

A. A. Friesem, Y. Amitai, “Planar diffractive elements for compact optics,” in Trends in Optics: Research, Developments and Applications, A. Consortini, ed. (Academic, San Diego, Calif., 1996), pp. 125–144.

Ghesquiers, J.-P.

S. Paineau, J.-P. Ghesquiers, M. Charrier, T. Lemoine, “Clock distribution by holographic optical backplane in massively parallel processor architecture,” in Free Space Micro-Optical Systems (European Optical Society, Engelberg, Switzerland, 1996), pp. 52–53.

Hagberg, M.

Hetherington, D.

Huang, A.

Huang, Y.-T.

Hugonin, J.-P.

Ichikawa, H.

Jaakkola, T.

Jacobs, B.

B. Jacobs, R. Zengerle, “Reactive ion etching of sloped sidewalls for surface emitting structures using a shadow mask technique,” J. Vac. Sci. Technol. B 14, 2537–2542 (1996).
[CrossRef]

Jahns, J.

S. J. Walker, J. Jahns, “Optical clock distribution using integrated free-space optics, ” Opt. Commun. 90, 359–371(1992).
[CrossRef]

J. Jahns, A. Huang, “Planar integration of free-space optical components, ” Appl. Opt. 28, 1602–1605 (1989).
[CrossRef] [PubMed]

Kato, M.

Katoh, Y.

Kostuk, R. K.

Kubota, T.

Kuisma, S.

Larsson, A.

Launois, H.

Lemoine, T.

S. Paineau, J.-P. Ghesquiers, M. Charrier, T. Lemoine, “Clock distribution by holographic optical backplane in massively parallel processor architecture,” in Free Space Micro-Optical Systems (European Optical Society, Engelberg, Switzerland, 1996), pp. 52–53.

Li, M.

Merz, J. L.

T. Takamori, L. A. Coldren, J. L. Merz, “Angled etching of GaAs/AlGaAs by conventional Cl2 reactive ion etching,” Appl. Phys. Lett. 53, 2549–2551 (1988).
[CrossRef]

Miller, J. M.

J. M. Miller, N. de Beaucoudrey, P. Chavel, E. Cambril, H. Launois, “Synthesis of a subwavelength-pulse-width spatially modulated array illuminator for 0.633 μm,” Opt. Lett. 21, 1399–1401 (1996).
[CrossRef] [PubMed]

J. M. Miller, J. Turunen, E. Noponen, A. Vasara, M. R. Taghizadeh, “Rigorous modal theory for multiply grooved lamellar gratings, ” Opt. Commun. 111, 526–535(1994).
[CrossRef]

A. Vasara, M. R. Taghizadeh, J. Turunen, J. Westerholm, E. Noponen, H. Ichikawa, J. M. Miller, T. Jaakkola, S. Kuisma, “Binary surface-relief gratings for array illumination in digital optics,” Appl. Opt. 31, 3320–3336 (1992).
[CrossRef] [PubMed]

E. Noponen, A. Vasara, J. Turunen, J. M. Miller, M. R. Taghizadeh, “Synthetic diffractive optics in the resonance domain, ” J. Opt. Soc. Am. A 9, 1206–1213 (1992).
[CrossRef]

J. M. Miller, N. de Beaucoudrey, P. Chavel, M. François, J. Turunen, “Inclined binary high-frequency gratings for an optical backplane interconnect,” in Proceedings of a Workshop on Diffractive Optics, Prague, Czech Republic, August 1995, pp. 33–34.

N. de Beaucoudrey, J. M. Miller, P. Chavel, J. Turunen, “On the design and fabrication of high efficiency inclined binary high frequency gratings,” in Specification, Production, and Testing of Optical Components and Systems, A. E. Gee, J. Houee, eds., Proc. SPIE2775, 533–536 (1996).

Nakaya, T.

Natarajan, S.

S. Natarajan, C. Zhao, R. T. Chen, “Bi-directional optical backplane bus for general purpose multi-processor board-to-board optoelectronic interconnects, ” J. Lightwave Technol. 13, 1031–1040 (1995).
[CrossRef]

Nishihara, H.

J. Saarinen, E. Noponen, J. Turunen, T. Suhara, H. Nishihara, “Asymmetric beam deflection by doubly grooved binary gratings, ” Appl. Opt. 33, 2401–2405 (1995).
[CrossRef]

Noponen, E.

Paineau, S.

S. Paineau, J.-P. Ghesquiers, M. Charrier, T. Lemoine, “Clock distribution by holographic optical backplane in massively parallel processor architecture,” in Free Space Micro-Optical Systems (European Optical Society, Engelberg, Switzerland, 1996), pp. 52–53.

Parker, J. W.

J. W. Parker, “Optical interconnection for advanced processor systems: a review of the esprit ii olives program, ” J. Lightwave Technol. 9, 1764–1773 (1991).
[CrossRef]

Pekola, J.

E. Tervonen, J. Turunen, J. Pekola, “Pulse-frequency-modulated high-frequency-carrier diffractive elements for pattern projection,” Opt. Eng. 33, 2579–2587 (1994).
[CrossRef]

Rentschler, J. A.

L. A. Coldren, J. A. Rentschler, “Directional reactive-ion etching of InP with Cl2 containing gases, ” J. Vac. Sci. Technol. 19, 225–230 (1981).
[CrossRef]

Saarinen, J.

J. Saarinen, E. Noponen, J. Turunen, T. Suhara, H. Nishihara, “Asymmetric beam deflection by doubly grooved binary gratings, ” Appl. Opt. 33, 2401–2405 (1995).
[CrossRef]

Suhara, T.

J. Saarinen, E. Noponen, J. Turunen, T. Suhara, H. Nishihara, “Asymmetric beam deflection by doubly grooved binary gratings, ” Appl. Opt. 33, 2401–2405 (1995).
[CrossRef]

Taghizadeh, M. R.

Takamori, T.

T. Takamori, L. A. Coldren, J. L. Merz, “Angled etching of GaAs/AlGaAs by conventional Cl2 reactive ion etching,” Appl. Phys. Lett. 53, 2549–2551 (1988).
[CrossRef]

Takeda, M.

Tervonen, E.

E. Tervonen, J. Turunen, J. Pekola, “Pulse-frequency-modulated high-frequency-carrier diffractive elements for pattern projection,” Opt. Eng. 33, 2579–2587 (1994).
[CrossRef]

Turunen, J.

J. Saarinen, E. Noponen, J. Turunen, T. Suhara, H. Nishihara, “Asymmetric beam deflection by doubly grooved binary gratings, ” Appl. Opt. 33, 2401–2405 (1995).
[CrossRef]

J. M. Miller, J. Turunen, E. Noponen, A. Vasara, M. R. Taghizadeh, “Rigorous modal theory for multiply grooved lamellar gratings, ” Opt. Commun. 111, 526–535(1994).
[CrossRef]

E. Tervonen, J. Turunen, J. Pekola, “Pulse-frequency-modulated high-frequency-carrier diffractive elements for pattern projection,” Opt. Eng. 33, 2579–2587 (1994).
[CrossRef]

A. Vasara, M. R. Taghizadeh, J. Turunen, J. Westerholm, E. Noponen, H. Ichikawa, J. M. Miller, T. Jaakkola, S. Kuisma, “Binary surface-relief gratings for array illumination in digital optics,” Appl. Opt. 31, 3320–3336 (1992).
[CrossRef] [PubMed]

E. Noponen, J. Turunen, A. Vasara, “Parametric optimization of multilevel diffractive optical elements by electromagnetic theory, ” Appl. Opt. 31, 5910–5912 (1992).
[CrossRef] [PubMed]

E. Noponen, A. Vasara, J. Turunen, J. M. Miller, M. R. Taghizadeh, “Synthetic diffractive optics in the resonance domain, ” J. Opt. Soc. Am. A 9, 1206–1213 (1992).
[CrossRef]

J. Turunen, F. Wyrowski, “Diffractive optics: from promise to fruition,” in Trends in Optics: Research, Developments and Applications, A. Consortini, ed. (Academic, San Diego, Calif., 1996), pp. 111–123.

N. de Beaucoudrey, J. M. Miller, P. Chavel, J. Turunen, “On the design and fabrication of high efficiency inclined binary high frequency gratings,” in Specification, Production, and Testing of Optical Components and Systems, A. E. Gee, J. Houee, eds., Proc. SPIE2775, 533–536 (1996).

J. M. Miller, N. de Beaucoudrey, P. Chavel, M. François, J. Turunen, “Inclined binary high-frequency gratings for an optical backplane interconnect,” in Proceedings of a Workshop on Diffractive Optics, Prague, Czech Republic, August 1995, pp. 33–34.

Vasara, A.

Walker, S. J.

S. J. Walker, J. Jahns, “Optical clock distribution using integrated free-space optics, ” Opt. Commun. 90, 359–371(1992).
[CrossRef]

Westerholm, J.

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, London, 1989), pp. 705–708.

Wyrowski, F.

J. Turunen, F. Wyrowski, “Diffractive optics: from promise to fruition,” in Trends in Optics: Research, Developments and Applications, A. Consortini, ed. (Academic, San Diego, Calif., 1996), pp. 111–123.

Yeh, J. H.

Zengerle, R.

B. Jacobs, R. Zengerle, “Reactive ion etching of sloped sidewalls for surface emitting structures using a shadow mask technique,” J. Vac. Sci. Technol. B 14, 2537–2542 (1996).
[CrossRef]

Zhao, C.

S. Natarajan, C. Zhao, R. T. Chen, “Bi-directional optical backplane bus for general purpose multi-processor board-to-board optoelectronic interconnects, ” J. Lightwave Technol. 13, 1031–1040 (1995).
[CrossRef]

Appl. Opt. (7)

Appl. Phys. Lett. (1)

T. Takamori, L. A. Coldren, J. L. Merz, “Angled etching of GaAs/AlGaAs by conventional Cl2 reactive ion etching,” Appl. Phys. Lett. 53, 2549–2551 (1988).
[CrossRef]

J. Lightwave Technol. (2)

S. Natarajan, C. Zhao, R. T. Chen, “Bi-directional optical backplane bus for general purpose multi-processor board-to-board optoelectronic interconnects, ” J. Lightwave Technol. 13, 1031–1040 (1995).
[CrossRef]

J. W. Parker, “Optical interconnection for advanced processor systems: a review of the esprit ii olives program, ” J. Lightwave Technol. 9, 1764–1773 (1991).
[CrossRef]

J. Opt. Soc. Am. A (2)

J. Vac. Sci. Technol. (1)

L. A. Coldren, J. A. Rentschler, “Directional reactive-ion etching of InP with Cl2 containing gases, ” J. Vac. Sci. Technol. 19, 225–230 (1981).
[CrossRef]

J. Vac. Sci. Technol. B (1)

B. Jacobs, R. Zengerle, “Reactive ion etching of sloped sidewalls for surface emitting structures using a shadow mask technique,” J. Vac. Sci. Technol. B 14, 2537–2542 (1996).
[CrossRef]

Opt. Commun. (2)

J. M. Miller, J. Turunen, E. Noponen, A. Vasara, M. R. Taghizadeh, “Rigorous modal theory for multiply grooved lamellar gratings, ” Opt. Commun. 111, 526–535(1994).
[CrossRef]

S. J. Walker, J. Jahns, “Optical clock distribution using integrated free-space optics, ” Opt. Commun. 90, 359–371(1992).
[CrossRef]

Opt. Eng. (1)

E. Tervonen, J. Turunen, J. Pekola, “Pulse-frequency-modulated high-frequency-carrier diffractive elements for pattern projection,” Opt. Eng. 33, 2579–2587 (1994).
[CrossRef]

Opt. Lett. (3)

Opto Laser Europe (1)

J. Bell, “Market misses message about diffractive optics,” Opto Laser Europe21–28 (March1997).

Other (8)

R. Petit, ed., Electromagnetic Theory of Gratings, Vol. 22 of Topics in Current Physics (Springer-Verlag, Berlin, 1980).
[CrossRef]

A. A. Friesem, Y. Amitai, “Planar diffractive elements for compact optics,” in Trends in Optics: Research, Developments and Applications, A. Consortini, ed. (Academic, San Diego, Calif., 1996), pp. 125–144.

J. Turunen, F. Wyrowski, “Diffractive optics: from promise to fruition,” in Trends in Optics: Research, Developments and Applications, A. Consortini, ed. (Academic, San Diego, Calif., 1996), pp. 111–123.

S. Paineau, J.-P. Ghesquiers, M. Charrier, T. Lemoine, “Clock distribution by holographic optical backplane in massively parallel processor architecture,” in Free Space Micro-Optical Systems (European Optical Society, Engelberg, Switzerland, 1996), pp. 52–53.

J. M. Miller, N. de Beaucoudrey, P. Chavel, M. François, J. Turunen, “Inclined binary high-frequency gratings for an optical backplane interconnect,” in Proceedings of a Workshop on Diffractive Optics, Prague, Czech Republic, August 1995, pp. 33–34.

N. de Beaucoudrey, J. M. Miller, P. Chavel, J. Turunen, “On the design and fabrication of high efficiency inclined binary high frequency gratings,” in Specification, Production, and Testing of Optical Components and Systems, A. E. Gee, J. Houee, eds., Proc. SPIE2775, 533–536 (1996).

D. Maystre, ed., Selected Papers on Diffraction Gratings, Vol. M583 of SPIE Milestone Series (SPIE Press, Bellingham, Wash., 1993), pp. xvii–xxx.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, London, 1989), pp. 705–708.

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Figures (12)

Fig. 1
Fig. 1

(a) General configuration for a planar optical backplane interconnection. (b) Ideal T1out,n and R0out,n for a system with N = 4 and M = 0.

Fig. 2
Fig. 2

Grating geometry for an optical backplane: propagating orders for (a) an output and (b) an input coupler.

Fig. 3
Fig. 3

Configuration for a slanted surface-relief grating.

Fig. 4
Fig. 4

Diffraction efficiencies of the k = 0, 1, 2 reflected and l = 1 transmitted orders for an output coupler in TE polarization as a function of (a) the relief depth, expressed as h/λ, for α and ff constant (α = −30° and ff = 0.5), (b) the grating slant angle α, for h and ff constant (h/λ = 1.058 and ff = 0.5), and (c) the fill factor ff, for h and α constant (h/λ = 1.058 and α = −30°). The numbered points in (b) and (c) denote the output-grating solutions for the backplane with N = 4 in Fig. 1(b).

Fig. 5
Fig. 5

Effect of a systematic error in h/λ on the performance of the backplane: uniformity error U, efficiency η, and efficiency lost into the k = 1 and k = 2 reflected order η1,lost (solid curve) and η2,lost (dashed curve).

Fig. 6
Fig. 6

Effect of a systematic error in the fill factor ff on the performance of the backplane.

Fig. 7
Fig. 7

Effect of a systematic error in the slant angle α on the performance of the backplane.

Fig. 8
Fig. 8

Slanted binary gratings with nonparallel groove walls: (a) undercutting (β > 0), (b) overcutting (β < 0), (c) overcut profile with compensation, and (d) approximation with stacked binary lamellar profiles and varying fill factors with (1) nonslanted and (2) slanted sections.

Fig. 9
Fig. 9

Effects of overcutting (β < 0) and undercutting (β > 0), without compensation, on the performance of the backplane.

Fig. 10
Fig. 10

Effect of undercutting (β > 0) and overcutting (β < 0), with compensation, on the performance of the backplane.

Fig. 11
Fig. 11

SEM micrographs of a slanted surface-relief grating in photoresist generated by use of electron-beam writing and RIE: (a) cross section at the nonoblique perspective of the slanted-grating profile and (b) a close-up showing the rounded edges and slight undercut.

Fig. 12
Fig. 12

Calculated diffraction efficiencies for an output coupler as a function of h (in micrometers). Other grating parameters are Λx = 0.598 μm, α = −22°, ff ≈ 0.35, n0 = 1.52, n1 = 1.60, n2 = n3 = 1, θinc = −44.03°.

Tables (3)

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Table 1 High-Efficiency Output-Coupler Grating Parameters and Diffraction Efficiencies in TE and TM Polarizations with a Constant Fill Factor ffn

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Table 2 Output-Coupler Parameters and Performance Characteristics for a Backplane Composed of N = 4 and N = 8 Slanted Gratingsa

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Table 3 Experimental and Theoretical Diffraction Efficiencies for the Fabricated Slanted Grating Acting as Output Coupler or Input Coupler

Equations (9)

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T1out,n=N- n+1-1,         R0out,n=1-T1out,n,
Λx= - λnsub sin θinc.
η = n =1NR0out,n -1×R0out,n -2 ×··· × R0out,0 T1out,n,
U = Inmax- InminInmax+ Inmin,
η1,lost=n= 1NR0out,n-1× R0out,n -2× ··· × R0out,0 R1out,n,
η2,lost=n= 1NR0out,n-1× R0out,n -2× ··· × R0out,0 R2out,n,
n2x =n12when 0  x < cn22,when c  x < Λ,
αinit= 12arcsinn0n¯ sin θinc+ arcsinn0n¯ sin θinc+ lλn¯Λx,
n¯2= 12n12+n22.

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